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lu_decomposition.py
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"""Lower-Upper (LU) Decomposition."""
# lower–upper (LU) decomposition - https://en.wikipedia.org/wiki/LU_decomposition
import numpy
def LUDecompose(table):
# Table that contains our data
# Table has to be a square array so we need to check first
rows, columns = numpy.shape(table)
L = numpy.zeros((rows, columns))
U = numpy.zeros((rows, columns))
if rows != columns:
return []
for i in range(columns):
for j in range(i):
sum = 0
for k in range(j):
sum += L[i][k] * U[k][j]
L[i][j] = (table[i][j] - sum) / U[j][j]
L[i][i] = 1
for j in range(i, columns):
sum1 = 0
for k in range(i):
sum1 += L[i][k] * U[k][j]
U[i][j] = table[i][j] - sum1
return L, U
if __name__ == "__main__":
matrix = numpy.array([[2, -2, 1], [0, 1, 2], [5, 3, 1]])
L, U = LUDecompose(matrix)
print(L)
print(U)